Living just 35 miles from London, I ought to be able to tell you exactly where the cemetery is, but I've never seen it. Folks from other countries seem to know London better than I do. Isn't that often the way? Anyway, I hope you will find this helpful:
The pet cemetery was established in 1880. It is close to Victoria Gate (on the west side of it, I think) and the gravestones can be seen from Bayswater Road. So, if you are in Kensington Gardens, go out through Victoria Gate, turn left and walk along the pavement, looking left through the park railings (but taking care not to bump into a lampost!).
On this website you will see an old photo of the gravestones:
http://www.images-of-london.co.uk/jss/product.php?xProd=126
If you like maps, I suggest you take a look at these two:
1. Modern map of Hyde Park and Kensington Gardens:
http://www.serpentine.org.uk/routes/02b/
Scroll down to read very good notes about Hyde Parke and Kensington Gardens, including where the pet cemetery is. Also, click on the 'larger map' facility for a clearer view: I would say that the exact position of the cemetery is between the R of LANCASTER GATE and the B of BAYSWATER ROAD.
2. Old map of the same area (between 1874 and 1882):
http://old-maps.co.uk/
Once there, do a place name search for Bayswater; on the next screen select the 'Bayswater, Middlesex' option; when you get the small map click three times on the right arrow (to the right of the map); then click on the 'Enlarged View' button below the map; then scroll the large Ordnance Survey map for an excellent look at the park and gardens at about the time the pet cemetery was established, ie about 20 years before Barrie met the Davies boys there. Going back one step, there is also a 'View Aerial Photo' button which you might like to try, although you cannot make out the cemetery in it.